Advertisements
Advertisements
Question
Draw a circle of radius 3 cm. Take any point K on it. Draw a tangent to the circle from point K without using center of the circle.
Solution
Analysis:
As shown in the figure, line l is a tangent to the circle at point K.
seg BK is a chord of the circle and ∠BAK is an inscribed angle.
By tangent secant angle theorem,
∠BAK = ∠BKR
By converse of tangent secant angle theorem,
If we draw ∠BKR such that ∠BKR = ∠BAK, then ray KR
i.e. (line l) is a tangent at point K.
Steps of construction:
- Draw a circle of radius 3 cm and take any point K on it.
- Draw chord BK of any length and an inscribed ∠BAK of any measure.
- By taking A as a centre and any convenient distance on the compass draw an arc intersecting the arms of ∠BAK in points P and Q.
- With K as a centre and the same distance in the compass, draw an arc intersecting the chord BK at point S.
- Taking radius equal to PQ and S as the centre, draw an arc intersecting the previously drawn arc. Name the point of intersection as R.
- Draw line RK. Line RK is the required tangent to the circle.
APPEARS IN
RELATED QUESTIONS
Draw a tangent at any point ‘P’ on the circle of radius 3.5 cm and centre O.
Draw a circle of radius 3.3 cm Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q. Write your observation about the tangents.
Select the correct alternative for the following question.
The maximum number of tangents that can be drawn to a circle from a point out side it is .............. .
Select the correct alternative for the following question.
(3) If ∆ABC ~ ∆PQR and `(AB)/(PQ) = 7/5`, then ...............
Draw any circle. Take any point A on it and construct tangent at A without using the centre of the circle.
Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.
Complete the following activity to draw a tangent to a circle at a point on the circle.
Draw a circle of radius 2.2 cm with O as centre.
↓
Take any point P on the circle and draw ray OP.
↓
Draw a perpendicular line to the ray at point P.
↓
Name the perpendilcular line as l
l is the tangent at point P.
Choose the correct alternative:
The tangents drawn at the end of a diameter of a circle are ______
Choose the correct alternative:
Which theorem is used while constructing a tangent to the circle by using center of a circle?
Draw a circle of radius 3 cm and draw a tangent to the circle from point P on the circle
| Draw a circle and take any point P on the circle. Draw ray OP |
| ↓ |
| Draw perpendicular to ray OP from point P |
| Draw a circle with center O and radius 3 cm |
| ↓ |
| Take any point P on the circle |
| ↓ |
| Draw ray OP |
| ↓ |
| Draw perpendicular to ray OP from point P |
Draw a circle of radius 4.2 cm. Draw a tangent to the circle at point P on the circle without using the center of the circle
Draw a circle with a diameter AB of length 6 cm. Draw a tangent to the circle from the end points of the diameter.
Draw a circle with center P. Draw an arc AB of 100° measure. Perform the following steps to draw tangents to the circle from points A and B.
- Draw a circle with any radius and center P.
- Take any point A on the circle.
- Draw ray PB such ∠APB = 100°.
- Draw perpendicular to ray PA from point A.
- Draw perpendicular to ray PB from point B.
Do the following activity to draw tangents to the circle without using the center of the circle.
- Draw a circle with radius 3.5 cm and take any point C on it.
- Draw chord CB and an inscribed angle CAB.
- With the center A and any convenient radius, draw an arc intersecting the sides of angle BAC in points M and N.
- Using the same radius, draw an arc intersecting the chord CB at point R.
- Taking the radius equal to d(MN) and center R, draw an arc intersecting the arc drawn in the previous step. Let D be the point of intersection of these arcs. Draw line CD. Line CD is the required tangent to the circle.
Draw a circle with center O and radius 3.4. Draw a chord MN of length 5.7 cm in a circle. Draw tangents to the circle from point M and N
Draw a circle of radius 4.2 cm. Draw a tangent to the circle from a point 7 cm away from the center of the circle
Take point P and Q and draw a circle passing through them. Draw a tangent AB to the circle without using the centre of the circle.
